2026 HGV P1 Q3

2026 HGV P1 Q3

Secondary 4
8 marks

The equation of a curve is \(y=3x^2-kx+k\), where \(k\) is a constant.

  1. Find the smallest value of the integer \(k\) for which the curve is always positive for all values of \(x\).[4]
  2. Find the set of values of \(k\) for which the line \(y=2x-2\) intersects the curve at two distinct points.[4]

Solution:

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Answer:(a) \(k=1\). (b) \(k<-2\) or \(k>10\).

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